Formation, compression and surface melting of colloidal clusters by active particles
Felix Kümmel, Parmida Shabestari, Celia Lozano, Giovanni Volpe & Clemens Bechinger
Soft Matter 11(31), 6187—6191 (2015)
We demonstrate with experiments and numerical simulations that the structure and dynamics of a suspension of passive particles is strongly altered by adding a very small (o1%) number of active particles. With increasing passive particle density, we observe first the formation of dynamic clusters comprised of passive particles being surrounded by active particles, then the merging and compression of these clusters, and eventually the local melting of crystalline regions by enclosed active particles.
The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
Scott Hottovy, Austin McDaniel, Giovanni Volpe & Jan Wehr
Communications in Mathematical Physics 336(3), 1259—1283 (2015)
We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driven by both white and Ornstein–Uhlenbeck colored noises. We discuss applications of the main theorem to several physical phenomena, including the experimental study of Brownian motion in a diffusion gradient.